What is the integral of sin(x)-sqrt(x) ?

The integral of sin(x)-sqrt(x) is -cos(x)-2/3 x^{3/2}+C

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integral of sin(x)-sqrt(x)

\int sin (x) - x d x

- cos (x) - \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int sin (x) - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (x) d x - \int x d x

\int sin (x) d x = - cos (x)

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= - cos (x) - \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - cos (x) - \frac{2}{3} x^{\frac{3}{2}} + C

What is the integral of sin(x)-sqrt(x) ?
The integral of sin(x)-sqrt(x) is -cos(x)-2/3 x^{3/2}+C